Re: Math and the mysterious
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I think it's a bit of an anthropic principle cannard. If mathematics weren't useful in describing the world, it never would have been developed.
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First, I'm not sure exactly what you mean by "cannard". (BTW the term, or concept of "anthropic principle" was first used maybe 10 years after this particular article was written). In any case, I agree that the "anthropic princlple" is actually a very rational attempt for an explanation of such problems, but in fact it is a kind of axiomatic argument. You can invoke the "anthropic princple" to explain any piece of evidence, "mysterious" as can be, and therfore it isn't "rational" in any real sense. I truely believe that Wigner would not accept it as a rational explantion for the problem he presents, but only as some more "sophisticated" version of an explanation of the form: "what is - must be (because we are to watch it)", which you can't say is more rational than saying "this is what krishna decided", or something to that effect.
I think that the deep point that Wigner is trying to make here, is that the connection between math (as we know it and use it) and phenomena is not obvious at all, as opposed to some suggestions on this thread. The argument that the universe has "order", and so "does math", and therefore they "fit", also doesn't hold and it's really the easiest way out of the question. If you read Wigner's article you can see why he choosed to use words such as "mysterious", and "no rational explanation" (and also "miracle", later on in the article). The fact the such a prominent scientist has chosen to use these specific words (it was a very provocative statement by him) should also be considered.
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